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A047921 Triangle of numbers a(n,k) = number of permutations on n letters containing k 3-sequences (n >= 0, 0<=k<=max(0,n-2)).

%I A047921 #15 Apr 20 2021 17:06:00
%S A047921 1,1,2,5,1,21,2,1,106,11,2,1,643,62,12,2,1,4547,406,71,13,2,1,36696,
%T A047921 3046,481,80,14,2,1,332769,25737,3708,559,89,15,2,1,3349507,242094,
%U A047921 32028,4414,640,98,16,2,1,37054436,2510733,306723,38893,5164,724,107,17,2,1
%N A047921 Triangle of numbers a(n,k) = number of permutations on n letters containing k 3-sequences (n >= 0, 0<=k<=max(0,n-2)).
%H A047921 J. Riordan, <a href="http://projecteuclid.org/euclid.bams/1183507357">Permutations without 3-sequences</a>, Bull. Amer. Math. Soc., 51 (1945), 745-748.
%F A047921 Riordan gives a recurrence.
%e A047921 Triangle begins:
%e A047921        1;
%e A047921        1;
%e A047921        2;
%e A047921        5,     1;
%e A047921       21,     2,    1;
%e A047921      106,    11,    2,   1;
%e A047921      643,    62,   12,   2,  1;
%e A047921     4547,   406,   71,  13,  2,  1;
%e A047921    36696,  3046,  481,  80, 14,  2, 1;
%e A047921   332769, 25737, 3708, 559, 89, 15, 2, 1;
%e A047921   ...
%Y A047921 Columns give A002628, A002629, A002630.
%Y A047921 Row sums give A000142.
%K A047921 nonn,tabf,nice,easy
%O A047921 0,3
%A A047921 _N. J. A. Sloane_
%E A047921 Edited and extended by _Max Alekseyev_, Sep 05 2010
%E A047921 a(0,0) = a(1,0) = 1 prepended by _Alois P. Heinz_, Apr 20 2021